Psych 215 Exam Three
If 12 participants solved anagrams on green paper and 14 participants solved anagrams on red paper. The degrees of freedom for the independent-samples t test would be
24
The results of a t test for two independent groups are summarized as t(64)=1.723, p> .05. Based on this you would know that the total number of participants in the study was________.
66
If part of an APA report is t(8)= 2.44 from paired-samples t test, how many participants were there in the study?
9 The value in the parentheses is degrees of freedom, and df=N-1. So N=df+1 for related-samples t test. If this were to be an independent-samples t test, N=df+2 =10, because df=N-2.
How does the shape of the t distribution compared to the (standard) normal distribution?
The t distribution is flatter and more spread out, especially if N is small
Which of the following is a fundamental difference between the t statistic and the z statistic?
The t statistic uses estimated standard error in the calculation
-Question: How are the z statistic and the t statistic similar? -Answer: They both are used to determine the number of standard deviations(standard error) that a sample mean deviates from the population mean stated in the null hypothesis in a sampling distribution. Decide whether the above answer is true.
True
related samples t test
compares means from the same group at different times
independent samples t test
compares the means for two groups
Which of the following is suitable for an independent-samples t test?
comparing performance scores for 6-year-old boys and 6-year-old girls
for tind, H0
corresponds to the situation where the independent variable has no effect
a critical value
defines the start point of a rejection region
difference between means
difference between Xbar 1 and Xbar 2 allows us to infer difference between mean 1 and mean 2
The sampling distribution of two-samples t test is a distribution of
differences of sample means
z test sample non-significant finding & interpretation
do not reject H0 (do not accept H1) interpretation: we did not find significant evidence that these patients mean flexibility score is different from 45 (dont say n=45) sampling error is probably why sample mean initially appeared to be different from population mean (we did not find that the sample mean is significantly different from population mean)
significant statistical test result
does not necessarily provide support for the research hypothesis in a study
within-subjects design
each subject gets all levels of IV/all conditions (most cases) same groups of subjects for all conditions variations: -same subject is observed in all conditions -same subject is observed before and after a "treatment" -observations on subjects are not independent -0 within-subjects design - t test for related samples - trel
between-subjects design
each subject gets one level of IV/one condition different groups of subjects for different conditions 0t-test for independent samples - tind
one-tailed test
entire rejection region is in one tail different hypothesis - directional hypothesis test whether parking time gets longer not just different
which of the following is a type II error?
fail to reject a false null hypothesis
If our study had a different finding is due to sampling error, it indicates a weakness of our study, for example, we did not select the best sample. Is this statement about sampling error true or false?
false
If the p value is larger than alpha, we would reject the null hypothesis.
false
If we write statistical hypotheses to test whether WI students spend 4 hours a day on social media as claimed by some research, then the null hypothesis will be about the WI students, and the alternative hypothesis will be about a non-student population.
false
The results of a hypothesis testing states "p= .23," this means the null hypothesis was rejected.
false
Type I and II errors occur because we made mistakes in our calculation of the test statistic.
false
Type I error happens because I made a wrong decision, for example, the observed statistic did not fall into the rejection region but I rejected the null hypothesis.
false
statistical significance also means scientific importance
false
statistically significant results are always desirable
false
type I error can also be called "false negative"
false
Alpha is the probability of finding certain or more extreme sample means.
false. The p value is the probability of finding certain or more extreme sample means, not alpha.
the power of a statistical test is defined as the probability of rejected H0 when it is ____ and H1 is ____
false; true
I research students' online learning experiences on psychology by giving out a survey to 20 first year students, 20 sophomores, 20 juniors and 20 seniors. Identify the levels included in the IV.
four levels in the IV: first year, sophomore, junior, and senior These four are the "levels," so when name your IV, try not to just list the levels, because levels are the VALUES included in the IV/characteristic, and the IV should be the name of that characteristic (SUMMARIZE the levels).
I research students' online learning experiences on psychology by giving out a survey to 20 first year students, 20 sophomores, 20 juniors and 20 seniors. Write down the IV(s).
i have one IV - "year in school" Or your own language to name the IV that summarizes all the levels "first year, sophomore, junior, and senior"
Which of the following if it is the case, has to be stated explicitly in the result reports?
if it is a one-tailed test
z test (reject null hypothesis)
if we know the p-value of the test statistic, we can compare with alpha value if p<=alpha (p<.05) - statistically rare or statistically significant. if <=5% changed you'd get that sample mean (tells us H0 is probably NOT true, reject H0) OR we don't have to calculate the p-value, but compare observed statistic with critical value
What is the last step in conducting a statistical hypothesis test?
interpreting the test results in the context of the original question
A pooled sample variance for the independent-samples t test
is not simply adding up the two sample variance, is used to calculate the estimated standard error, take into consideration of different sample size in calculation
alpha
is the standard that helps to determine whether a sample mean is rare.
which of the following is true about the result of changing alpha from 5% to 1% with nothing else changed?
it becomes less likely to reject the null hypothesis
The incomes of trainees at a local mill are normally distributed with a mean of $1,100. You collected a random sample of 4 female trainees and found their average salary is $900, with a standard deviation of $150. You wanted to find out whether the average salary of female trainees is less than $1100 a month. According to class, what is the symbol for $150 in this question?
symbol = s
the calculated numerical value that is compared to a table value in a hypothesis test is called the
test statistic
one sample t test
tests the means of a single group against a known mean
which of the following would likely be a within-subjects design?
the IV involves a repeated measure, experiences using Facebook and Instagram from the same group of students, personality test scores from twins
If my study involves testing whether activities done before an exam have any effect on students' exam scores. Which of the following is a Type I error?
the activities did not affect students' exam performance, but I claim they did, based on my hypothesis test
If you are doing a statistical test, then the hypotheses of the test will be about
the characteristics of a population such as the population mean
the boundaries of the rejection region or regions are specified by
the critical values
in the calculation of t statistic for related samples, the D means
the difference for each pair of scores
Which of the following is true about the result of changing alpha from 5% to 1%, with nothing else changed?
it becomes less likely you will reject the null hypothesis. Test statistic won't be affected by this change, because it is calculated from our study; but alpha exists outside of any study, for it is just a subjective standard used to compare with test statistic. The other false answers state the opposite directions.
The results of a hypothesis test are reported as: "t(20)= 2.70, p< .05." Which of the following is true regarding the value 2.70 above?
it is the observed t statistic
rejection regions
middle .95 is do not reject, the two tailed sides are .25 which means you reject the null hypothesis values on the sampling distribution that has p<.05 samples mean values that lead to reject H0 two rejection regions (for default two tailed tests) when x bar falls into either region meaning statistically significant results for p<.05, reject H0 critical value defines the critical region
When two groups are used in an experiment, the number of subjects in each group is indicated by ________.
n1 and n2
The results of a t test for two independent groups are summarized as t(64)=1.723, p> .05. Based on this you would know that the null hypothesis was
not rejected
The statistical symbol H0 is used to represent a(n) ______ hypothesis
null
a non-significant statistical test results means that
null hypothesis is not rejected
if zOBS falls into a rejection region, then the _____ hypothesis is ____.
null;rejected
If an experimenter sets alpha equal to .10, this means that he defines a "statistically rare" event as
occurring 10 or fewer times in 100 times if the null hypothesis is true.
College students' scores on an intelligence test are normally distributed with a mean of 100 and a standard deviation of 15. You collected a sample of 64 students from UWW to test whether UWW students has a higher IQ test performance in average. What statistical hypothesis test should you perform? In addition, should it be one-tailed test or two-tailed test "by default?"
one sample z test; two-tailed
what test is used as an alternative to the one sample z test when the population variance is unknown?
one-sample t test
You collected a sample of 64 students from UWW to test whether UWW students has a higher self esteem score than the national college student samples reported in the news. What statistical hypothesis test should you perform?
one-sample t test. Population standard deviation is unknown (so a z test won't work), but sample standard deviation can always be calculated, so a t test would work. No IV, not manipulation, cannot be two samples t test. In other words, the national sample is NOT part of "your" study (not the second sample/group/condition/level), just offers a context to introduce the value being tested against.
Why do we need to know the concept of rejection region in a two-tailed test? A）This concept gives us a simpler way to decide whether to reject the null hypothesis without looking up the z table/without find the probability associated with the sample mean. B) If we convert the obtained sample mean into a z statistic, we will know whether this z statistic falls into either rejection region (because we know the critical value of z at a certain alpha level, and can compare with the z statistic calculated), and therefore decide whether we should rejection the null hypothesis. C) It helps to define the alpha. D) it helps to find the p value.
only A) and B) As a researcher, we always set the alpha or the criterion first, and we can do that even before data collection. As long as alpha is set (e.g., alpha= .05), and we know the sampling distribution (here it is a normal distribution) and how many tailed test, the rejection regions are set, e.g., any z values that beyond +/- 1.96 for alpha= .05 (or any associated raw score values corresponding to such z values if we label the x axis with raw score values not z scores) in a two-tailed test. So C) is incorrect. The use of rejection rejection is to help us circumvent finding the p value of our observed statistic, so D) is incorrect.
The degrees of freedom in a related-samples t test A) is N-1 B) is the same as in an independent-samples t test C) is the same as in a one-sample t test
only A) and C) are correct
Regarding the following p-values, for which ones the null hypothesis H0 will be rejected at alpha = .10 level?
p=.03, p=.001, p=.06. all have a p value that is less than .10 which is the current alpha level, so they are small enough to allow rejecting the null hypothesis.
For a 2-tailed z test, the critical values of z at alpha level =.05 are
positive and negative 1.96
What is the correct decision if the statistical test produces a z statistic that is in the rejection region?
reject the null hypothesis
A researchers measures the time it takes 13 men and 15 women to complete multiple tasks in a study. As in the last question, with alpha=.05, what the researcher's decision would be if he reports the t test statistic is 2.558?
reject the null hypothesis and accept the alternative hypothesis
degrees of freedom for a statistic refers to the number of _____ that are free to vary when calculating the statistic
scores in the sample
In related-samples t tests, which of the following is the same as in independent-samples t tests?
statistical hypotheses
problems with statistical hypothesis testing
statistically significant is the probability that the result is compatible with the null hypothesis is very small the likelihood of a chance finding that will not hold up in future replications (if H0 is true) arbitrary alpha value significance does not tell us directly how big the difference was
steps to writing statistical hypotheses
step 1: write down two statistical hypotheses (the null hypothesis, alternate hypothesis, whether they are mutually exclusive) TWO TAILED TEST BY DEFAULT step 2: decision to reject or not reject H0 (reject H0 - means we found real difference), try to decide the probability (p-value) of getting this sample mean given the population mean (H0) is a specific value if the probability is too small "rare/unlikely", really unlikely to get an extreme sample mean step 3: write statistical significance sentence and p-value computation
t test steps
step one: one sample t-test state null and alternate hypothesis step two: calculate t statistic - find tobs step three: decision: reject H0, and accept H1 go further to interpret in terms of original problem the time it takes to find parking significantly different than 15 minutes this year the sample mean of 18 minutes is from a population with a mean different from 15 minutes difference between sample mean and population mean is significant at the .05 level
z test steps
step one: write down two statistical hypotheses step two: calculate the statistic step three: compare zcrit to zobs step four: make decisions about H0 (we either: reject H0 and accept H1, or do not reject H0, fail reject H0 and H1 not accepted) step five: interpretation in terms of the original question (population mean of UWW campus is significantly different from 250 OR the population mean of UWW campus is significantly higher than 250)
one characteristic of the two hypotheses formulated for a statistical test is that the hypotheses must
be mutually exclusive
in a nondirectional trel test, a rejection region to located in ____ of the sampling distribution of t
both tails
If our sample size is 39, what would be the critical value for a one-sample t test at alpha =.01? ( Look up in the t-table to answer this question)
+/- 2.750
A researchers measures the time it takes 13men and 15women to complete multiple tasks in a study. What is the critical value for this test if he conducts a two-tailed test at a .05 level of significance?
+/-2.056
Suppose a two-tailed z test was performed and the null hypothesis rejected with a significance level of .05. Which of the following could have been the value of the observed z statistic in the statistical test?
-1.98
one sample t test if standard deviation is known
-one sample t test - estimated s/square root of N -no longer z distribution -cannot use z statistic (use t statistic instead, usually provided for us) -sxbar is the estimator standard error -t distribution varies with degrees of freedom (df)
chapter 8 material
-tested whether a population parameter is a specific value -understand the logic of statistical hypothesis testing (H0 & H1), alpha & p-value, rejection region & critical value -perform one-sample z test and t test to identify situations in which a z test and t test may be used, understand test results reported in APA format
If I report an observed t statistic as 2.41 from a study that has a degrees of freedom of 8. The effect size eta squared will be
.42
If a study was run on 15 students from a campus that has 10,000 students . What would be the degrees of freedom for conducting a one-sample t test?
14
if an independent-samples t test was conducted on data from 20 students in a study. the degrees of freedom (df) is
18
What is the value for the degrees of freedom for a study comparing 10 UWW students' scores and 10 UWM students's cores and a study involving 18 participants observed two times?
18; 17
How many statistical hypotheses are there in a statistical hypothesis testing?
2
The results of a hypothesis test are reported as: "t(20)= 2.70, p< .05." How many participants were in the sample?
21
A) If we want to reduce the Type I error, Type II error will increase。 B) We always want to reduce Type I error. C) It is possible to reduce both Type I error and Type II error at the same time. Which of these statements is correct?
A
A) If I measure whether UWW students have an average sleeping time of 8 hours per night, B) If I measure whether UWW students have different amount of sleep time compared with UWM students C) If I measure whether UWW students have different amount of sleep in their dorms versus at home The appropriate statistical tests in order will be
A) a one-sample t test; B) an independent-samples t test; C) a related-samples t test
In what ways the results from different t tests(one-sample, independent samples and related samples) similar in the APA report? A) the observed test statistic is always reported, but not the critical value B) the df is always reported C) Information on the p value is always provided
A, B, C
How do we know whether we should reject a null hypothesis? A) Check whether the z observed statistics is more extreme than the critical value B) Check whether the p value of getting the sample mean or more extreme is equal to or smaller than the set alpha level C) Check whether the sample mean falls into a rejection region
A, B, and C
If I study whether listening to relaxed music or reading magazines before a exam helps with test performance, and my results show an effect size of eta squared=.42, which of the following is INCORRECT? A) The type of the activities did before the test in my study accounted for 42% of the variance in participants' test performance. B) The type of the activities did before the test in my study reduced participants' test performance by 42%. C)Knowing the activity participants did before the test resulted in a 42% reduction of the total variance in the study. D) 58% of the variance of participants' performance are due to factors other than the activities prior to the exam in the study (that we don't yet know). E) if the effect size were to be 1 in this context, it would mean that the activities participants did before exam fully explain why participants performed differently in that exam.
B All answers except B are correct, and are consistent with each other. A) is what covered in the video. C) is the interpretation offered in your text, e.g., on page 217 "conclusion." D) is a little indirect, and I put it here to explain what C) really means. If you understand the other options, then E) would make sense.
What does it mean if changing the alpha level from .05 to .01? A) this makes it easier to reject the null hypothesis B) this changes the observed t statistic C) this makes critical value(s) farther away from the center of the sampling distribution D) this makes rejection regions larger
C
Write statistical hypotheses for this question using appropriate notation on your own paper and check the answer later in the comments area: College students overall score 200 on a particular cognitive test with a standard deviation of 12. Are scores for the population of college students in Chicago different? We collected a sample of 35 students and found their average score is 220.
H 0: μ c h i c a g o= 200 H 1: μ c h i c a g o≠ 200 Note: the values be tested against is 200, not 220 because that is a sample mean.
Write statistical hypotheses for this question using appropriate notation on your own paper and check the answer later in the comments area: For 6- to 18-year old children overall, the mean amount of time spent on the internet per week is 35.5 hours. However we found children from 100 religious families averagely spent 32.5 hours with a standard deviation of 10 hours. Does the mean time spent on the internet per week differ for children of religious families?
H 0: μ r e l i g i o u s= 35.5 hours H 1: μ r e l i g i o u s≠35.5 hours Note the value being tested against is not 32.5
Write statistical hypotheses for this question using appropriate notation on your own paper and check the answer later in the comments area: Caffeine typically alters people's heart rates by 15 beats per minute. Does caffeine differently alter the heart rates of a population of people who drink caffeine every day?
H 0H 0：μ d a i l yμ d a i l y=15 beats H 1H 1：μ d a i l yμ d a i l y≠≠15 beats Feel free to use your own subscript to differentiate the interested population (those who drink caffeine daily) from the "general" population who's heart rate can be changed at 15 beats per minute. Also it is OK if you do not add the word "beats" or "beats per minute" at the end.
You are doing a statistical hypothesis testing to find out whether average preschool children watch TV for 212 minutes per day. Which of the following would be an appropriate null hypothesis?
H0:u=212 minutes
You are doing a statistical hypothesis testing to find out whether average preschool children watch TV for 212 minutes per day. Which of the following would be an appropriate alternative hypothesis?
H0:μ≠212 minutes
Which of the following is the symbol for the alternative hypothesis?
H1
independent samples t test has a degrees of freedom of
N-2
"With alpha equal to .05, a two-tailed independent-samples t test showed similar number of days to lose 5 pounds between the Atkins diet (M=45.8, SD=5.2) and the South Beach diet (M=42.4, SD=5.1), t (62)=1.3, p=.63." From this result, we know
N=64 1.3 is the observed t statistic; df=62=N-2, so N=64; p=.63 too big, so failed to reject the null hypothesis
If calculated t statistic is -2.30, and the critical value is -2.052, what is the correct decision?
Reject the null hypothesis and accept the alternative hypothesis
Why we can't say "accept the null hypothesis" if our finding is not significant, instead we have to say "fail to reject" the null hypothesis?
Your answer should emphasize that, accepting the null hypothesis means the null hypothesis is true, that the population mean EQUALS the value we are testing. However, the testing result only shows no evidence to say the population mean is DIFFERENT from the value we are testing. We DO NOT know whether the population mean is exactly that specific value, because it can be a slightly different value, just not different enough to be significant.
If we compare music preference between men and women, this study would be most likely which type of design?
a between-subjects design
a rejection region is
a proportion of the sampling distribution containing the sample means that will cause rejection of the null hypothesis
in a within-subjects design,
a single group of subjects is given each level of the independent variable
When can we do an one-tailed test? Although the text indicates that as long as we have a directional hypothesis, in reality, we often need which of the following?
a theoretical reason or based on the literature that a directional hypothesis is reasonable
alpha
also called the significance level, it is a probability defines a "statistically rare" outcome of H0 is true conventional standards alpha = .05 or alpha = .01
a statement of what must be true if the null hypothesis is false is called a(n) _______ hypothesis
alternative
terminology
an IV is also called a factor (an IV/factor has >=2 levels/conditions/groups) number of subject in level 1: n1 number of subject in level 2: n2 total subject in experiment = N N=n1+n2
Which of the following is the correct order of some procedures in calculating the test statistic for a related-samples t test? a) Calculate the (estimated)variance for D b) Calculate the D for each pair of scores c) Calculate the (estimated)standard error of difference between related means and use that as the denominator for the t formula d) Calculate the sum of squares (SS) for each D from their mean
b, d, a, c This question would be useful to earn extra points in Exam 3, but concrete calculation is not required for online learning.
effect size
the magnitude of the impact of one variable on another effect size n squared: the proportion of variance in the dependent variable that is attributable to the effect of the independent variable small effect size: real, but difficult to detect, difference between the heights of 15-16 year old years in US medium effect size: large enough to be visible to the naked eye, difference between heights of 14-18 year old girls large effect size: grossily perceptible and therefore large, difference between heights of 13-18 year old girls
if tobs for the t test for two independent groups does not fall into a rejeciton region, then
the null hypothesis is not rejected
degrees of freedom
the number of components in a statistics calculation that are free to vary (df=N-1) to calculate t, we need s s has N-1 degrees of freedom sxbar has N-1 degrees of freedom t distribution has N-1 degrees of freedom
Suppose we know that in conducting a one-tailed test, the rejection region is located on the left-hand tail of the sampling distribution, in this case we also know that the alternative hypothesis would mostly like be
the population mean is lower than the value we are testing against
Imagine we performed a statistical hypothesis test and found that the p value = .001, what does p value refer to?
the probability of getting the specific or more extreme sample statistic if the null hypothesis is true
A researcher tested 25 participants and conducted a statistical hypothesis test on the effect of treatment. That test generates a z value of 1.77. Assuming it is a two-tailed test
the researcher should not reject the null hypothesis with either alpha = .05 or alpha = .01
The results of a hypothesis test are reported as: "t(20)= 2.70, p< .05." Which of the following is true?
the test was a t test
If we increase the value of alpha from .01 to .05
the type I error is more likely
A) A study can have more than one independent variable (IV) and more than one dependent variable (DV). B) An IV must have at least two levels. C) A study sometime does not have any IV, but will always have DV(s). D) Another term for a DV is "variable of interest."
these statements are all correct
Do children from single-parent families have higher self-esteem than children from two-parent families? Does tap water taste any different than bottled water? The most appropriate statistical tests involved for these two questions in order should be
tind:trel
a statistical decision
to either reject or not reject the null hypothesis
the ____ test may be used to statistically analyze the score of a one-factor within-subjects design with two levels of the independent variable
trel
Alpha is a criterion that we used to decide whether the result in our study is rare enough to reject the null hypothesis.
true
Both alpha and p-value are probabilities, but alpha is usually decided by the researcher whereas p-value needs to be found.
true
For a two-tailed test, alpha as an area or probability is split up and locates at the two tails of the distribution.
true
If an obtained sample mean falls into a rejection region, it means that the p-value of getting such a sample mean (or more extreme) is smaller than the significance level.
true
The center of the sampling distribution for a two-samples t test is 0.
true
The results of a hypothesis testing states "p< .05," this means the null hypothesis was rejected.``
true
The results of a hypothesis testing states "p= .002," this means the null hypothesis was rejected.
true
When we reject a null hypothesis, it might be a type I error.
true
I research students' online learning experience on psychology as well as their sleeping habits by giving out a survey to 20 first year students, 20 sophomores, 20 juniors and 20 seniors. In statistical language, there are
two dependent variables (DVs)
I study how gender and age affect one's ability of perceiving colors. In my statistical analysis, I have
two independent variables
a statistical test that locates rejection regions at both end of the sampling distribution is called a _____ test
two-tailed
two tailed v. one-tailed test
two-tailed: rejection regions in both tails of the distribution of the test statistic one-tailed: the entire rejection region in only one tail of the distribution of the test statistic. the tail that corresponds to the predicted direction. a prior decision (made with good reasons). we are not (just) interested in "difference" but have a solid often theoretical reason to setup directional statistical hypotheses. does not change the way you calculate your test statistic but how we write out statistical hypothesis changes become directional and change the critical value
To find the probability of getting a specific sample mean or more extreme when the null hypothesis is true, we need to
use the null hypothesis to set up the sampling distribution
t test
we do not know the population variance, our sample size is small n<30
If our calculated z statistic does not fall into rejection region, then
we do not reject the null hypothesis
z test
we know the population variance OR we do not know the population variance but our sample size is large n>30 if we have a sample size less than 30 and do not know the population variance, we must use a t-test
If our obtained sample mean falls into a rejection region,
we reject the null hypothesis and accept the alternative hypothesis
When do we accept the alternative hypothesis?
when we reject the null hypothesis, we will accept the alternative hypothesis at the same time We only have two decisions: reject or not reject the null hypothesis. But when we reject the null hypothesis it means we accept the alternative hypothesis, because ONE of these two hypotheses must be true, so if the null hypothesis is false, the alternative hypothesis must be true and therefore we accept it.
why is there degrees of freedom?
when we use the z statistic, there is only one sampling distribution but a family of t distributions varies with degrees of freedom
A researcher is predicting that his manipulation will increase scores. If he is doing an one-tailed t test, the rejection region for the test
would be entirely in the right-hand tail of the distribution
the null hypothesis for tind is H0:
μ1 = μ2